Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure

Effect of electron exchange on atomic ionization in a strong electric field

Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized. A simple model is analyzed demonstrating that the decay probability, compared to the case of a local (Hartree) atomic potential, increases by many orders of magnitude. As a result of such increase, the ratio of inner to outer electrons ionization probability became not too small. It is essential that the effect of exchange upon probability of inner electron ionization by strong electric field is proportional to the square of the number of outer electrons. It signals that in clusters the inner electron ionization by strong field, the very fact of which is manifested by e.g. high energy quanta emission, has to be essentially increased as compared to this process in gaseous atomic objects.Comment: 7 pages, 1 figur

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

Derivation of High Purity Neuronal Progenitors from Human Embryonic Stem Cells

The availability of human neuronal progenitors (hNPs) in high purity would greatly facilitate neuronal drug discovery and developmental studies, as well as cell replacement strategies for neurodegenerative diseases and conditions, such as spinal cord injury, stroke, Parkinson's disease, Alzheimer's disease, and Huntington's disease. Here we describe for the first time a method for producing hNPs in large quantity and high purity from human embryonic stem cells (hESCs) in feeder-free conditions, without the use of exogenous noggin, sonic hedgehog or analogs, rendering the process clinically compliant. The resulting population displays characteristic neuronal-specific markers. When allowed to spontaneously differentiate into neuronal subtypes in vitro, cholinergic, serotonergic, dopaminergic and/or noradrenergic, and medium spiny striatal neurons were observed. When transplanted into the injured spinal cord the hNPs survived, integrated into host tissue, and matured into a variety of neuronal subtypes. Our method of deriving neuronal progenitors from hESCs renders the process amenable to therapeutic and commercial use

Genetic epidemiology of SARS-CoV-2 transmission in renal dialysis units - a high risk community-hospital interface

OBJECTIVES: Patients requiring haemodialysis are at increased risk of serious illness with SARS-CoV-2 infection. To improve the understanding of transmission risks in six Scottish renal dialysis units, we utilised the rapid whole-genome sequencing data generated by the COG-UK consortium. METHODS: We combined geographical, temporal and genomic sequence data from the community and hospital to estimate the probability of infection originating from within the dialysis unit, the hospital or the community using Bayesian statistical modelling and compared these results to the details of epidemiological investigations. RESULTS: Of 671 patients, 60 (8.9%) became infected with SARS-CoV-2, of whom 16 (27%) died. Within-unit and community transmission were both evident and an instance of transmission from the wider hospital setting was also demonstrated. CONCLUSIONS: Near-real-time SARS-CoV-2 sequencing data can facilitate tailored infection prevention and control measures, which can be targeted at reducing risk in these settings